Problem: What number could replace $z$ below? $\dfrac{2}{4} = \dfrac{z}{8}$
Solution: The fraction on the left represents 2 out of 4 slices of a rectangular pie. What if we cut the pie into 8 slices instead? How many slices would result in the same amount of pie? We would need 4 slices. $\dfrac{2}{4} = \dfrac{4}{8}$ and so the answer is $4$ Another way to get the answer is to multiply by $\dfrac{2}{2}$ $\dfrac{2}{2} = \dfrac{1}{1} = 1$ so really we are multiplying by 1. The final equation is: $\dfrac{2}{4} \times \dfrac{2}{2} = \dfrac{4}{8} $ so our answer is $4$.